There are actually many places that one can buy stamps from in Singapore. If you are simply looking for postage stamps to send your letters, you can simply buy it from any post office or a self-service automated machine (SAM). SAMs are conveniently located all around the island and you can find them in shopping malls or at mrt stations. There is a minimum purchase though so one will have to buy quite a few of the postage labels. The ones sold at SAM are usually the adhesive postage labels and I don't think there is much philatelic interest in them even amongst stamp collectors.
If you are looking to buy the traditional kind of postage stamps for collecting, you can always buy it from Singpost's online store which is called VPost. Just search for the link to philatelic and you will be able to browse and buy a great deal of both local and foreign stamps. Delivery charges are pretty cheap and they usually reach my home in 3 working days.
Another source where I buy stamps from is EBay. I have spent lots of money buying postage stamps from EBay and have always received my stamps on time and in order. The prices are bait more steep compared to the actual prices they were originally sold at as the sellers have to make a profit at the end of the day. You can find tons of stamps on EBay and they include both used as well as mint stamps.
I have also heard that some countries even have a system where you can buy stamps online and then print out the postage stamps to use. Now how cool is that?